Internal problem ID [5550]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-3 \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+4*y(x)=3*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 22
DSolve[y''[x]+4*y[x]==3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)+c_1 \cos (2 x)+c_2 \sin (2 x) \\ \end{align*}